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One of the most outstanding facts of observation of the distribution of temperature in the atmosphere is the constancy of the mean lapse-rate of temperature at all heights within the troposphere and in all latitudes. The variation about the mean value, which is roughly one-half of the dry adiabatic lapse-rate, is very slight at all heights greater than a few hundred metres above the ground, but in the layer nearest the ground the extent of the variation is very considerable. At night, and particularly during clear nights in winter, the sign of the lapse-rate in the lowest layer is changed, and the temperature increases with height instead of decreasing. On sunny summer afternoons the lapse-rate in the lowest layers attains very high values, the change of temperature from 1/2 metre to 1 metre above the ground amounting to the equivalent of 100 to 200 times the dry adiabatic lapse-rate. Observations in the layers still nearer to the ground are not yet available, but the nature of the values hitherto observed suggests that the lapse-rate increases in a marked manner as we approach the surface. This raises a very natural question. Is there any limit to the lapse-rate which physically capable of foundation in the atmosphere immediately above the ground? In an earlier paper, I have shown that the outward flux of heat (W-radiation) by radiation can be represented by —k ∂͞T/∂͞z calories/cm.2 /min., wherek is 115/pm at a temperature of 275° A.,pw being the vapour pressure in millibars, and T representing the absolute temperature at a height z above the ground. The average amount of incoming radiation which has to be disposed of is given (loc. cit .) as 0∙275 calories/cm.2 /min. This, however, is the average over all latitudes, and over day and night, and is too low a value for our present purposes. We shall adopt instead an amount equal to black body radiation at 280° A. amounting to 0∙509 calories/cm.2 /min. Of this, an amount 0∙290 calories/cm.2 /min. leaves the ground as W-radiation. These figures would roughly correspond with afternoon sunshine in the British Isles. If we assume the temperature gradient in the layer near the ground to be ∂͞T/∂͞z, then it has been shown (loc. cit .) that in this layer the amount of W-radiation transported outward by radiative diffusion is —1/2k ∂͞T/∂͞z. If the lapse-rate has the value given by the equation.

Some phenomena connected with the transfer of heat by radiation and turbulence in the lower atmosphere